Nonlinear Factor Returns in the US Equity Market

We examine nonlinear return-to-characteristic relationships for five equity market factors: value, momentum, small size, low beta, and profitability. Our study employs monthly returns and characteristics for the largest one thousand US stocks from 1964 to 2023 with a focus on average active returns over the last 20 years. Beyond simplicity in modeling the return-generating process, we find no reason to assume a linear relationship between characteristics and security returns. Allowance for nonlinearity leads to increases in information ratios for factor portfolios neutralized with respect to nonlinear exposure to the other factors.